With such platforms, both the topological bulk and boundary effects described above have been explored in 1D quasiperiodic chains, see Fig. REF . Specifically, using coupled photonics waveguide arrays, [cf. review by Szameit], topological phase transitions and topological equivalence between different quasiperiodic chains at smooth boundaries were explored, see Fig. REF (a) and Ref. [1]}.
Using a similar platform, (i) the relation of 1D quasiperiodic chains to 1D topological pumps and the associated associated topological boundary states of quasiperiodic chains, were explored [2]}, [3]}; (ii) The 0D topological boundary states were used to generate a high-fidelity on-chip Hong-Ou-Mandel interference of single-photons [4]} [cf. contribution on quantum]; (iii) Moving to 2D topological pumps, their predicted boundary phenomena with co-dimension 1 and 2 [5]}, was also observed using coupled photonic waveguide arrays [6]}, and their relationship to high-order topology was elucidated [7]}, [8]}. In the spirit of Fig. REF (b), topological boundary modes of quasiperiodic chains were also observed in polariton semiconductor microcavities [9]} [see Fig. REF (b), and acoustic chambers [10]}. In diffraction experiments, bulk gap labels of the 1D Fibonacci have been observed [11]}, see Fig. REF (b).
